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<p>Finds the hypervolume contribution for points in 3DD.  
 <a href="structshark_1_1_hypervolume_contribution3_d.html#details">More...</a></p>

<p><code>#include &lt;<a class="el" href="_hypervolume_contribution3_d_8h_source.html">shark/Algorithms/DirectSearch/Operators/Hypervolume/HypervolumeContribution3D.h</a>&gt;</code></p>
<table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a id="pub-methods" name="pub-methods"></a>
Public Member Functions</h2></td></tr>
<tr class="memitem:ac4d761c1d24708031664aff96129c043" id="r_ac4d761c1d24708031664aff96129c043"><td class="memTemplParams" colspan="2">template&lt;class Set , typename <a class="el" href="_c_svm_linear_8cpp.html#ab106d665148183a2dc94dcf8716c9203">VectorType</a> &gt; </td></tr>
<tr class="memitem:ac4d761c1d24708031664aff96129c043"><td class="memTemplItemLeft" align="right" valign="top">std::vector&lt; <a class="el" href="structshark_1_1_key_value_pair.html">KeyValuePair</a>&lt; double, std::size_t &gt; &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="structshark_1_1_hypervolume_contribution3_d.html#ac4d761c1d24708031664aff96129c043">smallest</a> (Set const &amp;points, std::size_t k, <a class="el" href="_c_svm_linear_8cpp.html#ab106d665148183a2dc94dcf8716c9203">VectorType</a> const &amp;ref) const</td></tr>
<tr class="memdesc:ac4d761c1d24708031664aff96129c043"><td class="mdescLeft">&#160;</td><td class="mdescRight">Returns the index of the points with smallest contribution as well as their contribution.  <br /></td></tr>
<tr class="separator:ac4d761c1d24708031664aff96129c043"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ad35f30562f9b12e8e85b9f4a268d39c3" id="r_ad35f30562f9b12e8e85b9f4a268d39c3"><td class="memTemplParams" colspan="2">template&lt;class Set &gt; </td></tr>
<tr class="memitem:ad35f30562f9b12e8e85b9f4a268d39c3"><td class="memTemplItemLeft" align="right" valign="top">std::vector&lt; <a class="el" href="structshark_1_1_key_value_pair.html">KeyValuePair</a>&lt; double, std::size_t &gt; &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="structshark_1_1_hypervolume_contribution3_d.html#ad35f30562f9b12e8e85b9f4a268d39c3">smallest</a> (Set const &amp;points, std::size_t k) const</td></tr>
<tr class="memdesc:ad35f30562f9b12e8e85b9f4a268d39c3"><td class="mdescLeft">&#160;</td><td class="mdescRight">Returns the index of the points with smallest contribution as well as their contribution.  <br /></td></tr>
<tr class="separator:ad35f30562f9b12e8e85b9f4a268d39c3"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a21b543685d2c16e733c932f8ca4f41d9" id="r_a21b543685d2c16e733c932f8ca4f41d9"><td class="memTemplParams" colspan="2">template&lt;class Set , typename <a class="el" href="_c_svm_linear_8cpp.html#ab106d665148183a2dc94dcf8716c9203">VectorType</a> &gt; </td></tr>
<tr class="memitem:a21b543685d2c16e733c932f8ca4f41d9"><td class="memTemplItemLeft" align="right" valign="top">std::vector&lt; <a class="el" href="structshark_1_1_key_value_pair.html">KeyValuePair</a>&lt; double, std::size_t &gt; &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="structshark_1_1_hypervolume_contribution3_d.html#a21b543685d2c16e733c932f8ca4f41d9">largest</a> (Set const &amp;points, std::size_t k, <a class="el" href="_c_svm_linear_8cpp.html#ab106d665148183a2dc94dcf8716c9203">VectorType</a> const &amp;ref) const</td></tr>
<tr class="memdesc:a21b543685d2c16e733c932f8ca4f41d9"><td class="mdescLeft">&#160;</td><td class="mdescRight">Returns the index of the points with largest contribution as well as their contribution.  <br /></td></tr>
<tr class="separator:a21b543685d2c16e733c932f8ca4f41d9"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a62366c7be907e3f5e409b010970e2913" id="r_a62366c7be907e3f5e409b010970e2913"><td class="memTemplParams" colspan="2">template&lt;class Set &gt; </td></tr>
<tr class="memitem:a62366c7be907e3f5e409b010970e2913"><td class="memTemplItemLeft" align="right" valign="top">std::vector&lt; <a class="el" href="structshark_1_1_key_value_pair.html">KeyValuePair</a>&lt; double, std::size_t &gt; &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="structshark_1_1_hypervolume_contribution3_d.html#a62366c7be907e3f5e409b010970e2913">largest</a> (Set const &amp;points, std::size_t k) const</td></tr>
<tr class="memdesc:a62366c7be907e3f5e409b010970e2913"><td class="mdescLeft">&#160;</td><td class="mdescRight">Returns the index of the points with largest contribution as well as their contribution.  <br /></td></tr>
<tr class="separator:a62366c7be907e3f5e409b010970e2913"><td class="memSeparator" colspan="2">&#160;</td></tr>
</table>
<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p>Finds the hypervolume contribution for points in 3DD. </p>
<p>The algorithm sweeps ascending through the z-direction and keeps track of of the current cut through the volume at a given z-value. the cut is partitioned in boxes representing parts of the hypervolume that is not hared with any other point. thus the sum of the volume of all boxes belonging to a point is making up its hypervolume.</p>
<p>The algorithm runs in O(n log(n)) time. </p>

<p class="definition">Definition at line <a class="el" href="_hypervolume_contribution3_d_8h_source.html#l00050">50</a> of file <a class="el" href="_hypervolume_contribution3_d_8h_source.html">HypervolumeContribution3D.h</a>.</p>
</div><h2 class="groupheader">Member Function Documentation</h2>
<a id="a62366c7be907e3f5e409b010970e2913" name="a62366c7be907e3f5e409b010970e2913"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a62366c7be907e3f5e409b010970e2913">&#9670;&#160;</a></span>largest() <span class="overload">[1/2]</span></h2>

<div class="memitem">
<div class="memproto">
<div class="memtemplate">
template&lt;class Set &gt; </div>
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  <td class="mlabels-left">
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          <td class="memname">std::vector&lt; <a class="el" href="structshark_1_1_key_value_pair.html">KeyValuePair</a>&lt; double, std::size_t &gt; &gt; shark::HypervolumeContribution3D::largest </td>
          <td>(</td>
          <td class="paramtype">Set const &amp;&#160;</td>
          <td class="paramname"><em>points</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">std::size_t&#160;</td>
          <td class="paramname"><em>k</em>&#160;</td>
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          <td>)</td>
          <td></td><td> const</td>
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<p>Returns the index of the points with largest contribution as well as their contribution. </p>
<p>As no reference point is given, the extremum points can not be computed and are never selected.</p>
<dl class="params"><dt>Parameters</dt><dd>
  <table class="params">
    <tr><td class="paramdir">[in]</td><td class="paramname">points</td><td>The set \(S\) of points from which to select the largest contributor. </td></tr>
    <tr><td class="paramdir">[in]</td><td class="paramname">k</td><td>The number of points to select. </td></tr>
  </table>
  </dd>
</dl>

<p class="definition">Definition at line <a class="el" href="_hypervolume_contribution3_d_8h_source.html#l00381">381</a> of file <a class="el" href="_hypervolume_contribution3_d_8h_source.html">HypervolumeContribution3D.h</a>.</p>

<p class="reference">References <a class="el" href="_exception_8h.html#adce1f80097c69010f5eab2618fa2e971">SHARK_RUNTIME_CHECK</a>.</p>

</div>
</div>
<a id="a21b543685d2c16e733c932f8ca4f41d9" name="a21b543685d2c16e733c932f8ca4f41d9"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a21b543685d2c16e733c932f8ca4f41d9">&#9670;&#160;</a></span>largest() <span class="overload">[2/2]</span></h2>

<div class="memitem">
<div class="memproto">
<div class="memtemplate">
template&lt;class Set , typename <a class="el" href="_c_svm_linear_8cpp.html#ab106d665148183a2dc94dcf8716c9203">VectorType</a> &gt; </div>
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  <td class="mlabels-left">
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          <td class="memname">std::vector&lt; <a class="el" href="structshark_1_1_key_value_pair.html">KeyValuePair</a>&lt; double, std::size_t &gt; &gt; shark::HypervolumeContribution3D::largest </td>
          <td>(</td>
          <td class="paramtype">Set const &amp;&#160;</td>
          <td class="paramname"><em>points</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">std::size_t&#160;</td>
          <td class="paramname"><em>k</em>, </td>
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        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype"><a class="el" href="_c_svm_linear_8cpp.html#ab106d665148183a2dc94dcf8716c9203">VectorType</a> const &amp;&#160;</td>
          <td class="paramname"><em>ref</em>&#160;</td>
        </tr>
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          <td></td>
          <td>)</td>
          <td></td><td> const</td>
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<p>Returns the index of the points with largest contribution as well as their contribution. </p>
<dl class="params"><dt>Parameters</dt><dd>
  <table class="params">
    <tr><td class="paramdir">[in]</td><td class="paramname">points</td><td>The set \(S\) of points from which to select the largest contributor. </td></tr>
    <tr><td class="paramdir">[in]</td><td class="paramname">k</td><td>The number of points to select. </td></tr>
    <tr><td class="paramdir">[in]</td><td class="paramname">ref</td><td>The reference Point \(\vec{r} \in \mathbb{R}^2\) for the hypervolume calculation, needs to fulfill: \( \forall s \in S: s \preceq \vec{r}\). </td></tr>
  </table>
  </dd>
</dl>

<p class="definition">Definition at line <a class="el" href="_hypervolume_contribution3_d_8h_source.html#l00355">355</a> of file <a class="el" href="_hypervolume_contribution3_d_8h_source.html">HypervolumeContribution3D.h</a>.</p>

<p class="reference">Referenced by <a class="el" href="structshark_1_1_hypervolume_contribution.html#aeee807833c090414b2c6dc41c1f8eca6">shark::HypervolumeContribution::largest()</a>, and <a class="el" href="structshark_1_1_hypervolume_contribution.html#ad7aba98bf20f20f16135b2e2f3b5ea2b">shark::HypervolumeContribution::largest()</a>.</p>

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<a id="ad35f30562f9b12e8e85b9f4a268d39c3" name="ad35f30562f9b12e8e85b9f4a268d39c3"></a>
<h2 class="memtitle"><span class="permalink"><a href="#ad35f30562f9b12e8e85b9f4a268d39c3">&#9670;&#160;</a></span>smallest() <span class="overload">[1/2]</span></h2>

<div class="memitem">
<div class="memproto">
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template&lt;class Set &gt; </div>
<table class="mlabels">
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      <table class="memname">
        <tr>
          <td class="memname">std::vector&lt; <a class="el" href="structshark_1_1_key_value_pair.html">KeyValuePair</a>&lt; double, std::size_t &gt; &gt; shark::HypervolumeContribution3D::smallest </td>
          <td>(</td>
          <td class="paramtype">Set const &amp;&#160;</td>
          <td class="paramname"><em>points</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
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          <td class="paramtype">std::size_t&#160;</td>
          <td class="paramname"><em>k</em>&#160;</td>
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          <td></td>
          <td>)</td>
          <td></td><td> const</td>
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<p>Returns the index of the points with smallest contribution as well as their contribution. </p>
<p>As no reference point is given, the extremum points can not be computed and are never selected.</p>
<dl class="params"><dt>Parameters</dt><dd>
  <table class="params">
    <tr><td class="paramdir">[in]</td><td class="paramname">points</td><td>The set \(S\) of points from which to select the smallest contributor. </td></tr>
    <tr><td class="paramdir">[in]</td><td class="paramname">k</td><td>The number of points to select. </td></tr>
  </table>
  </dd>
</dl>

<p class="definition">Definition at line <a class="el" href="_hypervolume_contribution3_d_8h_source.html#l00305">305</a> of file <a class="el" href="_hypervolume_contribution3_d_8h_source.html">HypervolumeContribution3D.h</a>.</p>

<p class="reference">References <a class="el" href="_exception_8h.html#adce1f80097c69010f5eab2618fa2e971">SHARK_RUNTIME_CHECK</a>.</p>

</div>
</div>
<a id="ac4d761c1d24708031664aff96129c043" name="ac4d761c1d24708031664aff96129c043"></a>
<h2 class="memtitle"><span class="permalink"><a href="#ac4d761c1d24708031664aff96129c043">&#9670;&#160;</a></span>smallest() <span class="overload">[2/2]</span></h2>

<div class="memitem">
<div class="memproto">
<div class="memtemplate">
template&lt;class Set , typename <a class="el" href="_c_svm_linear_8cpp.html#ab106d665148183a2dc94dcf8716c9203">VectorType</a> &gt; </div>
<table class="mlabels">
  <tr>
  <td class="mlabels-left">
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        <tr>
          <td class="memname">std::vector&lt; <a class="el" href="structshark_1_1_key_value_pair.html">KeyValuePair</a>&lt; double, std::size_t &gt; &gt; shark::HypervolumeContribution3D::smallest </td>
          <td>(</td>
          <td class="paramtype">Set const &amp;&#160;</td>
          <td class="paramname"><em>points</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">std::size_t&#160;</td>
          <td class="paramname"><em>k</em>, </td>
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        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype"><a class="el" href="_c_svm_linear_8cpp.html#ab106d665148183a2dc94dcf8716c9203">VectorType</a> const &amp;&#160;</td>
          <td class="paramname"><em>ref</em>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td> const</td>
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<p>Returns the index of the points with smallest contribution as well as their contribution. </p>
<dl class="params"><dt>Parameters</dt><dd>
  <table class="params">
    <tr><td class="paramdir">[in]</td><td class="paramname">points</td><td>The set \(S\) of points from which to select the smallest contributor. </td></tr>
    <tr><td class="paramdir">[in]</td><td class="paramname">k</td><td>The number of points to select. </td></tr>
    <tr><td class="paramdir">[in]</td><td class="paramname">ref</td><td>The reference Point \(\vec{r} \in \mathbb{R}^2\) for the hypervolume calculation, needs to fulfill: \( \forall s \in S: s \preceq \vec{r}\). </td></tr>
  </table>
  </dd>
</dl>

<p class="definition">Definition at line <a class="el" href="_hypervolume_contribution3_d_8h_source.html#l00280">280</a> of file <a class="el" href="_hypervolume_contribution3_d_8h_source.html">HypervolumeContribution3D.h</a>.</p>

<p class="reference">References <a class="el" href="_exception_8h.html#adce1f80097c69010f5eab2618fa2e971">SHARK_RUNTIME_CHECK</a>.</p>

<p class="reference">Referenced by <a class="el" href="structshark_1_1_hypervolume_contribution.html#acbf96ebbdb6fb438fb2efe64b235967d">shark::HypervolumeContribution::smallest()</a>, and <a class="el" href="structshark_1_1_hypervolume_contribution.html#a46626da682183658b940865fd4589506">shark::HypervolumeContribution::smallest()</a>.</p>

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</div>
<hr/>The documentation for this struct was generated from the following file:<ul>
<li>include/shark/Algorithms/DirectSearch/Operators/Hypervolume/<a class="el" href="_hypervolume_contribution3_d_8h_source.html">HypervolumeContribution3D.h</a></li>
</ul>
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